The comprehensive apology comes four years after the women launched legal action against the police, alleging the deception caused them emotional trauma.

As part of an out of court settlement, Martin Hewitt, an assistant commissioner at the Met, issued a statement saying: “Thanks in large part to the courage and tenacity of these women in bringing these matters to light it has become apparent that some officers, acting undercover whilst seeking to infiltrate protest groups, entered into long-term intimate sexual relationships with women which were abusive, deceitful, manipulative and wrong.

“I acknowledge that these relationships were a violation of the women’s human rights, an abuse of police power and caused significant trauma. I unreservedly apologise on behalf of the Metropolitan police service. I am aware that money alone cannot compensate the loss of time, their hurt or the feelings of abuse caused by these relationships.”

He added: “Most importantly, relationships like these should never have happened. They were wrong and were a gross violation of personal dignity and integrity.

“The Metropolitan police recognises that these cases demonstrate that there have been failures of supervision and management. The Metropolitan police recognises that this should never happen again and the necessary steps must be taken to ensure that it does not.”

He described the conduct of the undercover officers as “totally unacceptable” and conceded that the woman had been “deceived pure and simple”.

On Friday, the women said: “Although no amount of ‘sorry’, or financial compensation, can make up for what we and others have endured, we are pleased the police have been forced to acknowledge the abusive nature of these relationships and that they should never happen.

“By linking our cases together we have been able to evidence a clear pattern of abusive, discriminatory behaviour towards women which amounts to institutional sexism by the Metropolitan police.”

“Five years ago, it would have seemed inconceivable to the public that state employees would go to such lengths but the scale of abuse uncovered demonstrates that this was accepted practice for many years.“

The women have criticised police for obstructing legal action through a variety of tactics since they launched it in 2011. On Friday, Hewitt accepted that the legal proceedings “have been painful distressing and intrusive and added to the damage and distress. The women have conducted themselves throughout this process with integrity and absolute dignity.”

Who pays the price of police spies’ betrayals? | Letters

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The settlement is a significant moment in a controversy that has enveloped police since late 2010 when Mark Kennedy, the undercover spy who infiltrated environmental groups for seven years, was unmasked by activists.

The home secretary, Theresa May, has ordered a judge-led public inquiry to examine the undercover infiltration of political groups since 1968, after a series of revelations.

Kennedy was identified in the legal action as one of five undercover officers who concealed their real identities from their girlfriends during the relationships.One of the women, known only as Lisa Jones, had a six-year relationship with Kennedy before she and her friends exposed him. In her first media interview, she told the Guardian that gradually uncovering the truth about him felt like “long, slow painful torture – real psychological torture”.

Another undercover officer, Bob Lambert, had relationships with four women while pretending to be an animal rights and environmental activist for four years in the 1980s.

However, an eighth woman in the legal action, Kate Wilson, has not accepted the settlement and continues her legal fight. Wilson, who had a two-year relationship with Kennedy between 2003 and 2005, said that following the discovery of his real identity, “my sense of who I am and what I can believe, have been devastating and I remain haunted by unanswered questions”.

It is understood that the police did not disclose any documents about the covert deployments of the undercover officers during the legal case.

Other women who were deceived into having relationships with undercover officers have yet to settle their legal actions against the police.

The announcement on Friday follows an out of court settlement reached last year with a woman who was profoundly traumatised after finding out by chance that Lambert was the father of her son. The woman, known as Jacqui, was paid more than £400,000 by the Met. She had made the discovery 24 years after Lambert abandoned her and her son.